Stability and convergence in discrete convex monotone dynamical systems

We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is weaker than Lyapunov stability. Among others we show that the set of tangentially stable fixed points is isomorphic to a convex inf-semilattice, and a criterion is given for the existence of a unique tangentially stable fixed point. We also show that periods of tangentially stable periodic points are orders of permutations on $n$ letters, where $n$ is the dimension of the underlying space, and a sufficient condition for global convergence to periodic orbits is presented.Comment: 36 pages, 1 fugur

Ultrahigh spatial-frequency, high-contrast periodic structures produced by interference lithography

We have developed a process to produce high-aspect ratio, high- frequency periodic profiles recorded in a photoresist layer by interference lithography. We are able to independently control the period, duty cycle, and sidewall angle of the profiles. High-contrast diazonapthoquinone-based photoresist and single mode operation of the exposure laser are critical. The high-aspect ratio profiles are necessary for many applications such as transfer etch masks for etching oxides and field emitter array patterning. 5 refs., 5 figs

Effect of feeding three lysine to energy diets on growth, body composition and age at puberty in replacement gilts

This study evaluated the effect of diets differing in standard ileal digestible (SID) lysine on lysine intake, growth rate, body composition and age at puberty on maternal line gilts. Crossbred Large White×Landrace gilts (n =641) were fed corn-soybean diets differing in SID lysine concentration (%, g SID lysine:Mcal ME); diets were not isocaloric. Gilts received three grower, finisher diet combinations: low (0.68% lysine grower, 0.52% lysine finisher), medium (0.79% lysine grower, 0.60% lysine finisher) or high (0.90% lysine grower, 0.68% lysine finisher). Grower diets were fed from 100 until 142 days of age, and finisher diets were fed until they reached 220 days of age. Body weight (BW), backfat thickness (BF), and loin depth (LD) were recorded every 28 days. From 160–220 days of age, gilts were exposed daily to vasectomized boars and observed for behavioral estrus. Gilts fed the low lysine diet had lower average daily gain and BW (P \u3c 0.05), but not fat depth:LD ratio. The percentage of gilts that displayed natural estrus by 220 days of age was low but not different among dietary treatments (low 27.7%, medium 31.0% and high 37.7%, respectively; P=0.1201). Gilts fed the high and medium diets reached puberty 10 and 6 days earlier, however, than gilts fed the low lysine diet (P \u3c 0.05). The rate of puberty attainment may have been less because all gilts contracted porcine epidemic diarrhea (PEDv) just as boar exposure was to begin for the first group of gilts. Results from the present study indicate that growth rate and age at puberty can be altered by ad libitum fed diets that differ in SID lysine concentration

Polyakov Loops versus Hadronic States

The order parameter for the pure Yang-Mills phase transition is the Polyakov loop which encodes the symmetries of the Z_N center of the SU(N) gauge group. On the other side the physical degrees of freedom of any asymptotically free gauge theory are hadronic states. Using the Yang-Mills trace anomaly and the exact Z_N symmetry we construct a model able to communicate to the hadrons the information carried by the order parameter.Comment: RevTex4 2-col., 6 pages, 2 figures. Typos fixed and added a paragraph in the conclusion

Second Harmonic Generation for a Dilute Suspension of Coated Particles

We derive an expression for the effective second-harmonic coefficient of a dilute suspension of coated spherical particles. It is assumed that the coating material, but not the core or the host, has a nonlinear susceptibility for second-harmonic generation (SHG). The resulting compact expression shows the various factors affecting the effective SHG coefficient. The effective SHG per unit volume of nonlinear coating material is found to be greatly enhanced at certain frequencies, corresponding to the surface plasmon resonance of the coated particles. Similar expression is also derived for a dilute suspension of coated discs. For coating materials with third-harmonic (THG) coefficient, results for the effective THG coefficients are given for the cases of coated particles and coated discs.Comment: 11 pages, 3 figures; accepted for publication in Phys. Rev.

The equation of state for two flavor QCD at N_t=6

We calculate the two flavor equation of state for QCD on lattices with lattice spacing a=(6T)^{-1} and find that cutoff effects are substantially reduced compared to an earlier study using a=(4T)^{-1}. However, it is likely that significant cutoff effects remain. We fit the lattice data to expected forms of the free energy density for a second order phase transition at zero-quark-mass, which allows us to extrapolate the equation of state to m_q=0 and to extract the speed of sound. We find that the equation of state depends weakly on the quark mass for small quark mass.Comment: 24 pages, latex, 11 postscipt figure

Structure of the Quark Propagator at High Temperature

In the high temperature, chirally invariant phase of QCD, the quark propagator is shown to have two sets of poles with different dispersion relations. A reflection property in momentum space relates all derivatives at zero-momentum of the particle and hole energies, the particle and hole damping rates, and the particle and hole residues. No use is made of perturbation theory.Comment: 8 pages, Latex twocolum

1/N_c- expansion of the quark condensate at finite temperature

Previously the quark and meson properties in a many quark system at finite temperature have been studied within effective QCD approaches in the Hartree approximation. In the present paper we consider the influence of the mesonic correlations on the quark self-energy and on the quark propagator within a systematic $1/N_c$- expansion. Using a general separable ansatz for the nonlocal interaction, we derive a selfconsistent equation for the $1/N_c$ correction to the quark propagator. For a separable model with cut-off formfactor, we obtain a decrease of the condensate of the order of 20\% at zero temperature. A lowering the critical temperature for the onset of the chiral restoration transition due to the inclusion of mesonic correlations is obtained what seems to be closer to the results from lattice calculations.Comment: 19 pages, REVTeX, 5 figure

Solving Problems of Practice in Education

The authors identify and discuss the many complexities involved in the translation of scientific information in the social sciences into forms usable for solving problems of practice in education. As a means of appropriately handling these complexities and the issues that arise, they prescribe a series of stages to be followed from the advent of a practitioner's situational problem to the design of a response to it. They assert that unless the process of translation is conducted with the prescribed level of understanding, appreciation, and rigor, the application of knowledge will be inaccurate.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68934/2/10.1177_107554708400600103.pd

Does the QCD plasma contain propagating gluons?

Comparison of two appropriately chosen screening masses of colour singlet operators in the pure glue QCD plasma indicates that at sufficiently high temperature it contains a weakly-interacting massive quasi-particle with the quantum numbers of the electric gluon. Still in the deconfined phase, but closer to T_c, the same mass ratio is similar to that at zero temperature, indicating that the propagating modes are more glueball-like, albeit with a lower scale for the masses. We observe a continuity between these two regimes.Comment: 4 pages, 3 figure